The computation of \(\mathcal {T}\) , \(\mathcal {M}\) , \(\mathcal {S}\) , and \(\sigma \)  were performed
as follows. First, the orientations \(\theta _{\rm L}\)  and \(\theta _{\rm F}\)  are computed as described by Eq. REF  and detailed in Sect. REF  up to time \(T=2\times 10^6\)  for 20 sets of initial conditions. The values of \(\theta _{\rm L}\)  and \(\theta _{\rm F}\)  are then discretized by binning them into 6 bins on the interval \([0, 2\pi ]\)  (the use of 6 symbols was found to be sufficient to differentiate the behaviors of L and F while maintaining a computationally feasible number of sequences to be sampled to compute information measures, see [1]}, [2]}). For each set of initial conditions, the joint probability distribution of \(p(x(t), y(t), y(t+1))\) , from the time series, where \(x(t)\)  and \(y(t)\)  are the discretized forms of \(\theta _{i}\) , where \(x\)  and \(y\)  can be either \(L\)  or \(F\) . \(p(x(t), y(t), y(t+1))\)  is computed by counting the occurrences of each of the \(6^3\)  possible combinations of \((x(t), y(t), y(t+1))\)  and dividing by the total length of the time-series minus 1, \(2\times 10^6-1\) . Once the probability distributions are computed, \(\mathcal {T}\)  is computed by plugging them into the equation \(\mathcal {T}= \sum _{y_{t+\tau },y_t,x_t}p(y_{t+\tau },y_{t},x_t)\log _2 \frac{p(y_{t+\tau }|y_t,x_t)}{p(y_{t+\tau }|y_t)}\)  [3]}, where \(\tau =1\) . Likewise, \(\mathcal {M}\)  is computed using the formula \(\mathcal {M}=\sum _{x_t,y_{t+\tau }}p(x_t,y_{t+\tau })\log _2\frac{p(x_t,y_{t+\tau })}{p(x_t)p(y_{t+\tau })}\) .
